With deep divisions emerging in Theresa May's Cabinet over the hybrid customs partnership proposal, the CBI's director-general Carolyn Fairbairn welcomed Clark's intervention and called for "pragmatic solutions, not ideology".
European Union members (plus Turkey, Andorra, Monaco and San Marino) trade without customs duties, taxes or tariffs between themselves, and charge the same tariffs on imports from outside the EU.
But Tories who want to keep the United Kingdom inside the customs union are plotting to join the opposition Labour Party to defeat May in a crucial vote on the issue that could come later this month.
The UK government has admitted that the plan would be "unprecedented" and "challenging to implement".
Johnson further said: "It's totally untried and would make it very, very hard to do free trade deals".
"Instead of listening to vested interests he should pay more attention to the 17.4 million who voted to take back control of our trade policy".
A spokesman for the prime minister said May still had "full confidence" in Johnson, but pointed out that he and the rest of the Cabinet had previously supported the customs partnership proposal as a future option.
In what was being seen as a very public challenge to the Prime Minister's stance, Mr Johnson used an interview with the Daily Mail to warn that the customs partnership option would create a "whole new web of bureaucracy".
With less than a year to go before Britain leaves the bloc, May's Tory government remains deeply divided with a battle raging over future customs arrangements.
Could the issue topple May?
In a scathing assessment of the Foreign Secretary's behaviour, Mr Grieve concluded: "I don't think he is in any way prohibited by normal propriety in government".
Mr Clark told the Andrew Marr Show on Sunday that it was "absolutely right" that the United Kingdom leaves the customs union but added that "what we replace it with is of huge importance".
"Following last week's cabinet sub committee meeting, it was agreed that there are unresolved issues in relation to both models and that further work is needed".
Tory MP Bernard Jenkin told BBC Radio 4's Today programme that Mrs May was trying to bring the party together around the "compromise proposal" but he thought she would have to drop it.
Financial Times journalist James Blitz suggests that pro-Leave ministers may be making empty threats and recognise that May resigning is not in their best interests.
But is Johnson is getting exhausted of being the attack dog of the Brexiteers? "So their hands are tied". "But they know, too, that they can not bring Mrs May down, for fear of derailing Brexit altogether".